Estimation of rare events probabilities in computer experiments

We are interested in estimating probabilities of rare events in the context of computer experiments. These rare events depend on the output of a physical model with random input variables. Since the model is only known through an expensive black box function, standard efficient Monte Carlo estimates of rare events probabilities can not be used. We then propose two strategies to deal with this difficulty: a Bayesian estimate and an importance sampling method. Both proposals rely on Kriging metamodeling and are able to achieve sharp upper confidence bounds on the rare events probabilities. The variability due to the Kriging metamodeling step is properly taking into account. The proposed methodologies are applied to a toy example and a real case study which consists of finding an upper bound of the probability that the trajectory of an airborne load collides the aircraft that has released it.